document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843511>Question 843511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular courtyard of length 20m 16cm and breadth 15m 60cm is to be paved with same sized square tiles.Find the maximum possible numbers of such tiles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508572 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=508572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As long as we do not need to be realistic, there is no maximum number of tiles.<BR>\n" );
document.write( "In math-land my tiles could measure 1 nanometer by 1 nanometer, and I would use a huge number of those tiles.<BR>\n" );
document.write( " <BR>\n" );
document.write( "There is a minimum number of tiles, corresponding to a maximum tile size, if I am not allowed to cut the tiles into pieces.<BR>\n" );
document.write( " <BR>\n" );
document.write( "To line up a whole number of tiles along the 2016 cm length of the courtyard, I need square tiles with a side length that will go evenly into 2016 cm.<BR>\n" );
document.write( "To line up a whole number of tiles along the 1560 cm width of the courtyard, I need square tiles with a side length that will go evenly into 1560 cm.<BR>\n" );
document.write( "The tile side length on cm needs to be a factor of 2016 and 1560.<BR>\n" );
document.write( "The maximum tile size corresponds to the greatest common factor of 2016 and 1560.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2016=2%5E5%2A3%5E3%2A7 ALIGN=MIDDLE  ALT=\"2016=2%5E5%2A3%5E3%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1560=2%5E3%2A3%2A5%2A13 ALIGN=MIDDLE  ALT=\"1560=2%5E3%2A3%2A5%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The greatest common factor is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3%2A3=8%2A3=24 ALIGN=MIDDLE  ALT=\"2%5E3%2A3=8%2A3=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum tile size is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2824cm%29 ALIGN=MIDDLE  ALT=\"highlight%2824cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2824cm%29 ALIGN=MIDDLE  ALT=\"highlight%2824cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We would line up<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2016%2F24=2%5E5%2A3%5E3%2A7%2F%282%5E3%2A3%29=2%5E2%2A3%2A7=84 ALIGN=MIDDLE  ALT=\"2016%2F24=2%5E5%2A3%5E3%2A7%2F%282%5E3%2A3%29=2%5E2%2A3%2A7=84\"   DISABLED_style= \"max-width:90%; height:auto;\" > tiles along the length of the courtyard and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1560%2F24=2%5E3%2A3%2A5%2A13%2F%282%5E3%2A3%29=5%2A13=65 ALIGN=MIDDLE  ALT=\"1560%2F24=2%5E3%2A3%2A5%2A13%2F%282%5E3%2A3%29=5%2A13=65\"   DISABLED_style= \"max-width:90%; height:auto;\" > tiles along the width of the courtyard.<BR>\n" );
document.write( "That mean that we would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84%2A65=2%5E2%2A3%2A5%2A7%2A13=20%2A39=5460 ALIGN=MIDDLE  ALT=\"84%2A65=2%5E2%2A3%2A5%2A7%2A13=20%2A39=5460\"   DISABLED_style= \"max-width:90%; height:auto;\" > tiles.<BR>\n" );
document.write( "We can also calculate that the surface area of the 24-cm tiles is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824cm%29%2824cm%29=576cm%5E2 ALIGN=MIDDLE  ALT=\"%2824cm%29%2824cm%29=576cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "while the surface area of the courtyard is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282016cm%29%281560cm%29=3144960cm%5E2 ALIGN=MIDDLE  ALT=\"%282016cm%29%281560cm%29=3144960cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and that it would take<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3144960cm%5E2%2F%28576cm%5E2%29=5460 ALIGN=MIDDLE  ALT=\"3144960cm%5E2%2F%28576cm%5E2%29=5460\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the surface area of one tilew to cover the whole courtyard. </SPAN>\n" );
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